Noelle ran 4 1/2 miles in the morning and 3 1/4 miles in the evening. how far did noelle run that day? a student solved the problem this way: let n represent the total number of miles noelle ran. n = 4 1/2 + 3 1/4 n = 4 2/4 + 3 1/4 n = 7 3/4 noelle ran 7 3/4 miles that day. use a similar strategy to solve this problem. diane ran 3 1/8 miles on tuesday, 4 1/2 miles on wednesday, and 4 1/4 miles on thursday. what is the total distance diane ran in the 3 days? a. 12 8/7 miles b. 12 7/8 miles c. 5 3/4 miles d. 3 13/14 miles

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

$9.41

step-by-step explanation: